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Computational Mathematics and Modeling

, Volume 23, Issue 2, pp 125–132 | Cite as

A method to compute the electric field vector on the surface of the cardiac muscle

  • E. V. Zakharov
  • A. V. Kalinin
Mathematical Modeling

Methods of assessing the electrophysiological state of the heart by solving the inverse problem of electrocardiography in potential form are actively used in clinical practice. Some results suggest, however, that on its own the electric potential of the heart may not be sufficient for diagnosing complex cases of cardiac arrhythmia. Studies have shown that the absolute value of the potential gradient is an important characteristic that produces a more precise assessment of the electrophysiological state of the heart. In this article we propose an algorithm for numerical reconstruction of the potential gradients from the solution of the inverse problem of electrocardiography.

Keywords

inverse problem of electrocardiography boundary integral equation method potential gradient singular integral hypersingular integral 

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References

  1. 1.
    R. Barr and M. Spach, Inverse Solutions Directly in Terms of Potentials [Russian translation], Meditsina, Moscow (1979).Google Scholar
  2. 2.
    A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Application of Tikhonov regularization method for numerical solution of the inverse problem of electrocardiography,” Vestn. MGU, Ser. 15, Vychisl. Matem. Kibern., No. 2, 5–10 (2008).Google Scholar
  3. 3.
    A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Numerical methods for solving some inverse problems of the electrophysiology of the heart,” Diff. Uravn., 45, No. 7, 1014–1022 (2009).MathSciNetGoogle Scholar
  4. 4.
    E. V. Zakharov and A. V. Kalinin, “Numerical solution of a three-dimensional Dirichlet problem in a piecewise-homogeneous medium by boundary integral equation method,” Zh. Vychisl. Matem. Mat. Fiz., No. 7, 1197–1206 (2009).Google Scholar
  5. 5.
    A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Numerical solution of the inverse problem of electrocardiography for a medium with a piecewise-constant electrical conductivity,” Zh, Vychisl. Matem. Mat. Fiz., No. 7, 1233–1239 (2010).Google Scholar
  6. 6.
    A. V. Kalinin, “Iterative algorithm for the inverse problem of electrocardiography in a medium with piecewise-constant electrical conductivity,” Prikl. Matem. Informat., Izd. MGU, No. 34б, 35–40 (2010).Google Scholar
  7. 7.
    B. B. Punske, Q. Nu, R. L. Lux, R. S. MacLeod, et al., “Spatial methods of epicardial activation time determination in normal hearts,” Annals Biomed. Eng., 31, 781–792 (2003).CrossRefGoogle Scholar
  8. 8.
    E. V. Zakharov, A. G. Davydov, and I. V. Khaleeva, “Integral equations with Hadamard kernels in diffraction problems,” in: Topical Issues in Applied Mathematics [in Russian], Izd. MGU, Moscow (1989), pp. 118-127.Google Scholar
  9. 9.
    A. Sutradhar, G. H. Paulino, and L. J. Gray, Symmetric Galerkin Boundary Element Method, Springer (2008).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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